Number of even-length integer partitions of n with integer median.

Terms

a(0) =0a(1) =0a(2) =1a(3) =0a(4) =3a(5) =1a(6) =5a(7) =3a(8) =11a(9) =7a(10) =17a(11) =16a(12) =32a(13) =31a(14) =52a(15) =55a(16) =90a(17) =99a(18) =144a(19) =167a(20) =236a(21) =273a(22) =371a(23) =442a(24) =587a(25) =696a(26) =901a(27) =1078a(28) =1379a(29) =1651